You can have violence without killing people, for example in torture the goal is generally not to kill the recipient.
And if a doctor has a surgery that goes bad and the patient died, they may have killed someone, but there was no violence.
But you can't have killing without violence.
I guess if you get extremely broad with the term but starvation isn't often classified as violence.
If the starvation is intentional it's a kind of violence ?
Smallpox, radiation leaks, freezing to death etc are all causes of death that can be engineered but not generally labeled as violence. What definition are you using?